KOLLOID-ZEITSCHRIFT & ZEITSCHRIFT FUR POLYMERE ZUR

ZEIT

VEREINIGT

Band 186

MIT

DEN KOLLOID-BEIttEFTEN

9 ORGAN

DER

KOLLOID-GESELLSCHAFT

November 1962

Heft 1

Polymere F r o m the Chemstrand J~esearch Center, Inc., D u r h a m , North Carolina ( U S A )

Elastic Properties of Networks Formed from Oriented Chain Molecules Fibrous N a t u r a l R u b b e r

By A. Greene and A. Ci/erri With 9 figures in 21 details and 3 tables

(Received May 29, 1962)

Introduction Elastic properties of networks formed b y randomly cross-linking disoriented chain molecules (referred in the following for convenience as "normal" networks) have been extensively investigated (1, 2). The rubber elasticity theory has been found to satisfactorily represent their experimental behavior, although some discrepancies still exist. The present work attempts to systematically characterize the elastic properties of networks in which random cross-linking occurs while the macromolecules are maintained in an oriented state. The elastic properties of interest here are, however, those exhibited b y the network after the cause of orientation has been removed. To give a particular example, if a macromolecular material is cross-linked in the highly oriented crystalline state, the network we should consider is that obtained when the material is carried aboveits melting temperature and allowed to shrink under no external constraints. Theoretically the ease of networks formed from oriented chain molecules can be treated according to the general postulates of the rubber elasticity theory with due modifications taking into account the orientation of the chains during cross-linking. Two different ways in which this orientation can be achieved have been considered. According to one model, the cross-links are formed in a previously ordered structure where stretched out chain molecules are arranged in a parallel array (3). This model was associated with the cross-linking naturally occurring in fibrous proteins. The theory of elasticity for the system of macromolecules cross-linked in the p~rallel array and thereafter disoriented

without rearranging the cross-links (this system is referred in the following for convenience as "oriented" network), predicts that the force of retraction, /, in simple elongation is given b y the equations due to .Flory (3): Zi Li : v

(rO1( ' ) \

E,J

ro~ /

'~ ri

~

[2]

where L~ is the length of the sample in its disoriented isotropie state, v is the total number of chains in the network structure, a' to a good approximation is the number of chains in a cross-section perpendicular to the direction in which L~ is measured (for a given network a constant independent of elongation); rl2 is the mean-square end-to-end distance for a typical network chain and r02 is the corresponding value for the free chain unconstrained b y the cross-links, k, T and are the Boltzmann constant, the absolute temperature and the elongation ratio respectively. Eqn. [1], within the limit of the assumed gaussian statistics, applies to oriented as well as to normal networks. The effect of the degree of cross-linking on the isotropic length, Lt, is, however, an important difference between the two types of networks. In fact, fox the extreme case of perfect axial orientation a', in eqn. [2], will coincide with the number of macromoleeules in a crosssection and, therefore, will be independent of v. Since r02 is inversely proportional to v, L t is expected, in this case, to increase with v" (r~/~o2)'~. For a normal network, however,

2

Kolloid-Zeitschrifl und Zeitschriftfiir Polymere, Band 186 9Heft 1

a' is a function of v since on increasing the degree of cross-linking not only more chains are added to the system, b u t also more of them will intersect a given plane. An increase of a' as v~ ()-~2]~0~)t is required in order for L~ to be independent of v, as is experimentally verified for cross-linking normal networks [apart from a small density variation which accompanies the crosslinking process (4)]. From this theory it is evident that, in spite of the fact that L~ can be substantiMly increased for a system formed b y oriented macromolecnles, the resulting network is still considered to be isotropic and indistinguishable fl'om a normal network insofar as the dependence of stress or strain is concerned. This follows at once from the assumed gaussian statistics. Indeed, Lodge (5) has shown that any gaussian network should display isotropic elasticity. A second ease where chain molecules are cross-linked in an oriented state has been theoretically considered. This is the ease of the "composite" network, i.e. a network formed b y further cross-linking, in the stretched state, a network which had been previously cross-linked in the unstretehed isotropic state. The composite network was associated with the occnn'ence of an increase of the unstrained length (permanent set) acquired b y a strip of cross-linked rubber after it had been held stretched at high temperature. Andrews, Tobolsk~y and Hanson (6) postulated that this set was due to a partial degradation of the initial network with concurrent formation of new chains unstrained at the stretched length. Accordingly, they postulated that the decay of stress in a sample maintained at constant extension at an elevated temperature would be that expected in the absence of the crosslinking reaction. The resultant network was then visualized as a double network, the permanent set resulting from balancing of the refractive force of one network (unstrained at the original length and characterized b y the number of the original "first stage" crosslinks left unbroken) and the extensive force of a second network (unstretched a t the stretched length and characterized b y the number of "second stage" cross-links introduced). The simpler case of a composite network where cross-linking formation in the strained state is unaccompanied b y the degradation was rigorously treated b y Berry, Scanlan and Watson (7) and b y Fiery (8). These authors, assuming that all the chains

of the network were gaussian, substantiated the two-network hypothesis (6) and concluded that the composite gaussian network should display isotropic elasticity relative to the state of ease of the set material, the shape of the stress-strain isotherm being still determined b y the function a - I/a s (eqn. [1]). Scott and Stein (9), Scanlan and Watson (I0), Flory (8) and Scanlan (11) have considered the more complex case of rupture of first stage cross-links and formation of second stage cross-links in a given state of strain. They showed that the simple two-network hypothesis was not applicable to a composite network from which some of the first stage cross-linkages were removed. However, the previous conclusions about the isotropy and the shape of the stress-strain curve were not modified. On the experimental side tests of both these theories have been scarce. The postulated isotropy of composite networks was verified through equilibrium swelling measurements on composite natural rubber networks b y Berry, Scanlan and Watson (7). Ch~rIesby and yon A r n i m (12), however, performed stress-strain measurements on networks formed b y cross-linking natural rubber samples previously oriented in the calendering process and found the samples to have anisotropic elastic behavior. The results of Oth and Flory (13), who studied the stressstrain isotherm of natural rubber samples cross-linked in the fibrous (racked) state indicate a proportionality of the refractive force to the strain function ~ - 1/~ 2. Although this seems in agreement with eqn. [1], it appears to disagree with the behavior of normal networks, under similar experimental conditions, which is represented b y the well known equation (1, 2):

in which A is the initial cross-sectional area, V/L~, V being the volume of the sample. The presence in eqn. [3] of the additional term C~ has been attributed to the non-equilibrium character of the measurements which are usually performed (14). It is not clear, however, if the agreement found b y Oth and Flory between theory and experiment can be explained on the basis that for their oriented networks equilibrium conditions were more readily obtained than for normal networks. In this paper we present the results of a study of the elastic properties (equilibrium

Greene and Ciferri, Elastic Properties of 2Vetworks Formed from Oriented Chain Molecules

swelling and stress-strain-temperature analysis supplemented with some preliminary X - r a y a n d b i r e f r i n g e n c e m e a s u r e m e n t s ) for natural rubber networks cross-linked in the fibrous, racked state. This system has been c o n s i d e r e d as a s a t i s f a c t o r y a p p r o x i m a t i o n for the model of chains cross-linked in the parallel array which was used in the deriv a t i o n o f e q n s . [1] a n d [2] (3, !5). A c t u a l l y , s i n c e r a c k e d r u b b e r is n o t f o r m e d b y p a c k i n g together rod-like molecules but rather by stretching an initially amorphous network, t h e s y s t e m m i g h t also b e c o n s i d e r e d as a composite network. However, since the degree of cross-linking of the original amorp h o n s n e t w o r k is p r a c t i c a l l y z e r o ( a l t h o u g h e n t a n g l e m e n t s are, o f c o u r s e , p r e s e n t ) a n d since the degree of orientation of the racked s a m p l e is v e r y h i g h , t h i s s y s t e m c o u l d n o t b e r e g a r d e d as a t y p i c a l c o m p o s i t e n e t w o r k . The fibrous rubber presents a particular i n t e r e s t if, i n d e e d , i t c a n b e c o n s i d e r e d a s a model for the elastic behavior and contractility of fibrous proteins. In fact, experiments have confirmed the essential correctness of e q n . [2] f o r n a t u r a l r u b b e r (15) a n d p o l y e t h y l e n e (16) c r o s s - l i n k e d i n t h e o r i e n t e d s t a t e , as w e l l a s for c o l l a g e n (17) a n d k e r a t i n fibers (18). W h i l e n o e x p e r i m e n t a l e v i d e n c e was given for the isotropy of the disoriented networks of natural rubber, polyethylene and collagen, this condition was not apparently m e t b y t h e s u p e r c o n t r a e t e d k e r a t i n fibers, which made the agreement with the theory somewhat unexpected. The question of the isotropy of these networks deserves particular attention in view of the fact that they s h o w a p r e f e r e n t i a l a x i a l r e c r y s t a l l i z a t i o n (13, 16). T h i s w a s p a r t i c u l a r l y w e l l e v i d e n t i n t h e case of polyethylene samples cross-linked in t h e v e r y h i g h l y o r i e n t e d s t a t e (16), w h i c h could perform a cyclic process of contraction on melting and spontaneous elongation on crystallization.

Experimental Natural

Rubber

Backed natural rubber samples were prepared fl'om two different latex films, kindly supplied by Dr. L. Mandelkern. Samples prepared from one film are distinguished from samples prepared from the other film through the use of the initials a and b (table 1); in addition all racked samples are designated by the letter J?. The distinction between the two films was made because when uncross-linked racked samples prepared from film a were shrunk (see below) they recovered the originM dimensions better than samples from film b. This was taken as an indication either that polymer a had a higher molecular weight than polymer b or that

3

polymer a was slightly cross-linked (15). Racking was performed as described by ~oberts and Mandellcern (15). Strips about 4 cm long, 1 em wide and 0.2 cm thick were subjected to a very rapid elongation while being held at 80 ~ and then quickly cooled to about 20 ~ Oriented crystallization, as evidenced by X-ray measurements, took place rapidly at the lower temperatures and-this allowed the samples to maintain their orientation, even when the external tensile force was removed, up to a temperature of about 42 ~ at which the sample began to shrink. Ink marks, about 1 cm apart, were drawn in the central portion of the strips and the degree of orientation given to the samples was characterized by the ratio of the distance (measured in the direction of orientation) between these ink marks, after and before (L0) the racking process. This ratio, acr , is given in table 1 and it varies, for different samples, from about 3 to 14. Length measurements were made with a ruler allowing a precision of _+ 0.05 cm. Table 1 Characteristics of the Samples

Sample

cr

a-R4 a-R5 a-R12 a-R2 a-t~l

2.8 3.3 5.3 7.3 7.7

b-R7 b-/%6 b-R8

14.0 14.0 14.0

a-N N-6

1.0 1.0

dose 24 Mrads 24 M~ads 24 Mrads 24 Mrads 24 Mrads

cr (e) (e) (e) (e) (e)

2.1 2.3 2.8 3.1 3.2

8 Nrads (y) 24 ~rads (y) 24 Mrads (y)

2.9 3.4 3.5

24 Mrads (e) Sulfur-accelerator vulcanized 1)

1.0 1.0

1) Ingredients by weight: 100 rubber, 5.0 ZnO, 2.5 S, 1.0 mercaptobenzothiazole, 0.5 phenyl fl-naphthylamine: one hour at 110 ~ The central portion of the oriented strip was then cut off and its ends were taped (without further stretching) to a thin glass rod in order to prevent bending of the samples during cross-linking. Samples which did not show a constant cross-section in the direction of orientation were discarded. Samples were then sealed in vacuum for cross-linking. For samples of polymer a cross-linking was accomplished with the electron beam of a van de Gra] accelerator which allowed a very quick deposition of the desired dose (about 4 hrs.). The electron beam was scanned over the surface of the samples. Samples were, in this case, enclosed in a rectangular glass tube, in order to avoid the scattering of the electrons from curved glass surfaces. These precautions assured that the region occupied by the samples was homogeneously irradiated as was established by independent dosimetry measurements. In order to avoid the danger of heating the samples above 40 ~ during irradiation with the van de Gra~ accelerator a stream of compressed air was maintained around the rectangular glass tube and the total dose was given by steps, t~or samples of polymer b cross-linking was accomplished in a cylindrical Cos0 source giving a uniform 7 ray dose of about 0.5 • l0 s t%ads/hr. In this ease, no particular precautions were necessary to ensure that the samples were not overheated. Doses are listed on gable 1. The initial (e) denotes irradiation with the van de Graaff accelerator and the initial (y) denotes irra1"

4

Kolloid-Zeitschrift und Zeitschrift fiir Polymere, Band 186 9 Heft I

diation with the cobalt source. After cross-linking the samples were still crystalline, as evidenced by X-ray measurements 9 Shrinkage was obtained by immersing the samples for 1 minute in boiling water. Shrinkage took place very rapidly in these conditions, but in order to eliminate all residual slow relaxation processes and also all soluble, uncross-linked material (never exceeding 5%), the samples were allowed to reach equilibrium swelling in benzene which was then pumped off. The length of the samples after treatment with boiling water (designated by L]) did not change either after the treatment with benzene or after a period of several months 9 The set acquired was permanent in character. Also the elastic properties which were subsequently determined were qnite reproducible either immediately after shrinkage or after a period of several months. The degree of permanent set aequh'ed by the samples was characterized by the ratio a] = LI/Lo • e (table 1) where e is a correction factor introduced in order to compensate for an irrecoverable increase in length not associated with the cross-

were weighed and immersed in n-decane for I~3 days at 25 ~ The swollen strips were surface dried and reweighed9 Equilibrium values were generally obtained after 24 hrs. Swelling ratios, v, (relative volumes of unswollen to swollen strips) were calculated using densities of 09 and 09 for natural rubber and n-decane, respectively. In spite of the inaccuracy which would be expected from this method (surface drying in particular) the results proved to be accurately reproducible. Maximum error on v is of the order of + 0.005 (which comprises the presumed indetermination of 0.005 in the densities of each component) 9 The increase of length on swelling was measured simultaneously with tile measurement of swelling ratios and it was characterized by Z, ratio of the unswollen to the swollen length. (v/Z) ~/2 gives t2ae average linear swellings in the directions perpendicular to the orientation. g=Z--(v/Z)I~2/Z was used to characterize the swelling anisotropy of any given sample. Estimated error on g is of the order of • 2O/o. Values of v and g for the samples investigated are reported in table 2.

Table 2 Equilibrium Swelling Data (n-Decane at 25 ~ Sample

v

and Stress-Strain Data for Unswollen Samples at the Temperature Indicated Z

g%

a-l~4

09

0.662

5.3

a-R5 a-P~12 a-t~2 a-R1

0.266 0.27i 0.293 0.311

0.674 0.678 0.70t 09

6.8 6.8 7.8 8.5

b-t~7

0.167

0.613

14.8

2 Cx, kgcm -2 2 G~, kgem -~ 0.6 0.6 0.9 0.6 0.0 0.0

30 60 38 40 30 38

1.5

30 6O 60 38 30

b-~8

09

0.701

15.0

4.0

0.2 O.2 0.0

a-N N-6

0.253 0.295

0.632 0.667

0.0 0.3

1.9 3.1

1.4 2.3

19

linking process itself but rather with flow processes. The factor e which was determined for control, uncrosslinked samples racked in the same conditions as for the samples which were cross-linked, is the ratio of the length that the uncross-linked samples assumed after treatment with boiling water to the corresponding initial Lo. For samples from polymer a, e was taken equal to 1.3, and for sample from polymer b was taken equal to 2.0 . These values are, for each polymer, averages of three independent measurements, deviations from the averages being of the order of • 0.3. This results in an indetermination of a] values which limit too rigorous a quantitative comparison of the elastic properties of the various samples as a function of their a]. Also included in table 1 are two normal networks (designated with the letter 37) the elastic properties of which are reported for comparison with the elastic properties of oriented networks9 Sample a-N is a normal network of polymer a, cross-linked under the same conditions used for cross-linking the racked samples of polymer a. Sample N-6 is a normal sulfur vuleanizate, the composition of which is given in the table. Soluble material was removed from these samples as described above for oriented samples.

Equilibrium

Swelling

Equilibrium swelling measurements for natural rubber in n-decane (Matheson, Coleman & Bell) were performed following the technique described by Berry, Scanlan and Watson (7)9 Central portion of the strips

T,~

3.0 3.3 2.8 3.4 4.2 5.2

Dynamometry The dynamometer and the procedures for obtaining stress-straht isotherms and stress-temperature curves for samples unswollen and swollen with n-hexadeeane were essentially similar to those described in detail elsewhere (I4, I9}. The "standard procedure" described in conjunction with stress-strain measurements for normal rubber networks (14) was used (the sample was extended by successive increments, the tension being recorded after an interval of 3 minutes at each length) but the maximum elongation was not limited to cr ~ 2. Sometimes elongations up to a ~ 3 were reached9 The retraction phase of the standard procedure cycle ( 1 ) was also-generally performed although in most of the graphs it is not reported. Particular care was devoted to the measurement of the initial cross-sectional area of unswollen samples especially in view of possible variations along a given sample. A microscope equipped with a fdar micrometer, which permitted an accuracy within • 0.01 mm for individual measurements, was used for this end. Cross-sections were measured at intervals of 5 mm along the sample, the average value being used for converting the measured tension to stress, T, referred to the cross-section, A, of the unswollen, unstressed sample. Samples whose crosssection varied by more than 5% were discarded. A was in general of the order of 10 • 10 -3 cm ~. The value of the cross-sectional area was also checked from the weight and the length of each unswollen sample using the above value of density. Samples for investigation of the

Greene and Ciferri, Elastic Properties of Networks Formed from Oriented Chain Molecules effect of diluent Oil the stress-strain-temperature relationships were prepared by swelling a given crosslinked sample hi n-hexadeeane (Eastman Chemical Co.) until the desired amount was absorbed. The quantity of solvent thus absorbed was, however, less than the quantity that the given sample would absorb at equilibrium with excess n-hexadeeane. Both unswollen and swollen samples were analyzed while in an inert helium atmosphere. For swollen samples the weigh t of the sample was measured before and after any given experiment to ensure that the composition had not

b - R8,60 ~

b-

E

R8, 50 ~

o

b - RT, 3 0 ~

a - R2, 30*

o

R4 60

.f

z

f~C.

ca" 0.2

0.4

08

0.6

•

Fig. 1. Stress-strMn data for unswollen samples at the temperature indicated

changed appreciably during the course of the experiment. Stress-strain data are plotted as ~ vs cr and as For swollen samples the plotted values of * include a factor v ~18which arises from the fact that the stress was always referred to the unswollen, unstretched cross-

.

.

5

a similar one in order to assure that a typical pair had been determined. Since the linear portion of the

~/ (a - - ; ) vs.1/a plots is limited and in some case nonexistent, the procedure of representing the experimental data by the pair C 1 and C2 is entirely arbitrary. It was chosen, however, in order to afford a comparison with the results of normal networks which are usually represented in terms of C~ and Cs. Errors on C~ and C~ were estimated to be about • 0.2 kg/em 2. Repeated measurements on a given sample were reproducible within the limits of experimental errors and no essential change was noticed on increasing from 3 to 30 minutes the time interval at each length. In the case of stress-temperature measurements the sample was stretched and maintained at constant length at the highest experimental temperature (70 ~ until the tension appeared constant. A temperature cycle was then performed recording the values of tension at each temperature as soon as the tension appeared constant. Temperatures at which the tension was measured were in the order, 70, 60, 40, 30 and 50 ~ (-b 0.2). A complete cycle could be performed in about 2 hours. Experimental data are illustrated i n figs. 4, 5, 6. Since the length was kept constant during the temperature cycle and the initial unstrained length was measured at the average temperature T (50 ~ elongations given are correct at 50 ~ Determination of the unstressed length at 50 ~ before and after several hours following the completion of the cycle did not differ appreciably. It is evident from the graphs that for low elongations the plots are, within the limits of experimental en'ors, linear and no hysteresis is present. On increasing elongation, for any given sample, both the linearity relationship loses its accuracy and also some hysteresis appears. The elongation range investigated for each sample was, however, kept within the range in which said deviations barely become perceptible. From experiments not reported it was evident, particularly for unswollen samples, that at elongations above the range reported these deviations become more and more severe. Swollen samples invariably broke when higher stresses were applied. The absence of noticeable hysteresis in the low elongation region has been taken as support for applying thermodynamic analysis to stress-temperature data (1, 19). Accordingly, we have applied thermodynamic analysis to oar results disregarding the fact that for high elongations some small hysteresis was indeed noticeable. Values of the slopes (Ov/~T)p.L and the values of the stress, Y, at the average temperature, T, were calculated with the least square method and are listed on table 3. The values of the energy component (1, 2).

] V 11~

.

sectmn A, m whmh case the quantity ~ invsManttodilution according to (3) A

should be vl/[t

where a ) = - - ~ - - - are also listed on table 3 and are

T--

A

--

g

\~/

--~

[1']

where V, ri 2, r0~ and v refer to the unswollen state and a is the extension relative to the swollen rest state. Values of C 1 and C2 (eqn. [3]) were obtained, when possible, according to the eurren~ convention (14, 20), from the linear portion of the

~/ ( c r

1in plots

(figs. 1, 2), and are reported on table 2. Each pair of C~ and C~ refers to one particular experiment (the one illustrated in the graph). Several other measurements had been made, however, both on the same sample or on

reported as a function of ~ in fig.7. A n error on (OI-//aL)~, f

results from the use of the least square method in cases where deviation from linearity, in the ~ vs T plots, begin to appear. This, however, should not alter our conclusions as to the downturn of (OH/OL)p,~ (cf. seq.). The values of the energy component at constant volume (~E/O.L)v, Vy= ]e [which reflects the contribution from the intramolecular, conformational, energy (2, 19)] could not be determined directly. :However, a method for calculating ]e has been recently proposed which is valid for systems obeying the gaussian theory of rubber elasticity (eqns. [1], [1'])0 This is done

6

Kolloid-Zeitschrifl und Zeitschrift fi~r Polymere, Band 186 9 Heft I

according to the relationship (19) /

--

X-ray

~ . ~-p,z

~--1

[5]

which was applied for calculating t h e values of Jell listed on table 3. fl is t h e cubic expansion coefficient for the sample. For unswo]len samples this was t a k e n (21) equal to 6.6 • 10 -4 deg. -~ and for swollen samples it was calculated, from the particular composition, using a

~, 2

b - RS,v=0.39, 9

30~

~ b - R 7 , v=l, 3 0 ~

b -RT, v = 0 . 3 5 , I

I,

I

I

I

I

I

30 ~

I

I

I

I

I

I

E

c) a-Rl, v=I,38 ~

r~ 4 a -RI2,w

a- R5, v=1,38

~ ,

N - 6 , v = I , 3 0 ~' N - 6 , v =0.41, 3 0 ~

|

I

I 0.2

I

I

,I

0.4

~ 0.6

'

' 0.8

I

(2

Fig. 2. Effect of swelling with n-hexadeeane on the stress-strain isotherm. The swelling ratio a n d the temperature arc indicated. ( 0 ) Unswollen, ( 9 swollen value of 9.2 • 10-4 deg. -1 for n-hexadecane (22) assuming addltivity of volumes. I n all stress-strain a n d stress-temperature measurements t h e temperature was limited to 70~ in order to avoid degradation of samples. The lower limit (30 ~ was chosen because it appears above t h e equilibrium melting temperature, under no external stress, for similar oriented networks (13, 15).

Wide angle diffraction p a t t e r n s of samples at 25 ~ were obtained using a Siemens flat plate camera equipped with a pinhole collimating system. The X - r a y generating tube was operated at 35 K V a n d 14 milliamperes. Nickel filtered Cu radiation was used. Exposure time was from 30 to 45 minutes, t h e film-sample distance 4.3 cm a n d t h e incident X - r a y b e a m was normal to t h e direction of orientation (fiber axis) of the sample. The wide angle diffraction p a t t e r n of a racked uncross-linked sample of polymer b is reported in fig. 9a. I n this p a t t e r n t h e amorphous scatter is weak and diffraction spots typical of a single crystal with rotational s y m m e t r y a b o u t a n axis perpendicular to the incident X - r a y b e a m arc present. The occurrence of this p a t t e r n was a n additional proof of the high axial orientation of t h e racked samples, l~o evident change was observed in this diffraction p a t t e r n after t h e sample h a d been irradiated. The corresponding p a t t e r n for t h e s h r u n k e n sample b-R7, after t h e t r e a t m e n t designed to remove residual stresses a n d soluble material, is reported in fig. 9b. The p a t t e r n for the b-R8 sample swollen with n-hexadeeane (v ~ 0.4) is also included (fig. 9 c). B o t h p a t t e r n s are typical of amorphous scatter. Wide angle diffraction patterns for shrunken samples b-R7 a n d b-i~8 unswollen a n d swollen with n-hexadecane (v ~ 0.4) were also t a k e n while the material was maintained a t different elongations. I n this case the material was allowed to stay at 25 ~ for 2 hours at the given elongation before exposure to t h e X-ray. After X - r a y irradiation the sample was relaxed for two hours at 25 ~ before these operations were repeated a t another elongation. The object of these measurements was to find the m i n i m u m elongation at which diffraction spots could be visually observed in the X - r a y pattern. The limitations of this analysis are well realized a n d we regard the results obtained as preliminary ones. Diffraction p a t t e r n s were t a k e n for sample b-~7 unswollen at a ~ 1, a ~ 1.6, a ~ 1.8, a ~ 2.0, a n d c~ = 2.2 and for t h e same sample swollen at a = l , a : 1.6, a : 1.8, a = 2 . 0 , a n d a ~ 2.3. For sample b-R8 at a ~ 1, cr ~ 1.1, a = 1.3, a n d for the same sample swollen at a = 1, a = 1.2, and a = 1.3. Diffraction patterns are not reported since it would be difficult to reproduce the faint details of interest. I t was found t h a t on stretching the unswollen samples t h e diffraction p a t t e r n typical of amorphous scatter (fig. 9) gradually revert to the diffraction p a t t e r n of t h e racked sample. The first appearance of diffraction spots was observed for sample b-/t7 at a = 1.8. For the nnswollen sample b-/~8 very faint spots could be detected even at a ~ 1 and t h e y became more evident on increasing elongation. On stretching of swollen samples, however, no appearance of diffraction spots could be observed at the elongations investigated.

Bire/ringence Samples were examined, in the unstressed state, with a polarizing microscope equipped with a hot stage. The retardation was measured with a Derek type compensator. Racked uncross-linked samples were highly birefringent b u t t h e birefringence disappeared after the samples were maintained for a b o u t 1 hour at 50 ~ a n d it did not reappear at room temperature. The birefringence did not disappear, however, for shrunken cross-linked samples. R e t a r d a t i o n vs. t e m p e r a t u r e curves for shrunken, unswollen samples b-/~7 a n d b-lq8 are reported in fig. 8, (since the thickness of these sumples were very nearly the same, ~, 1 ram, retardation values were not converted to birefringence). }:or these measurements the samples were first allowed to

Greene and Ciferri, Elastic Properties of Networks Formed from Oriented Cttain Molecules

7

stay about one month at 0 ~ and then they were the orientation during cross-linking, the finM directly transferred to the polarizing microscope at set, al, also increases. At the same time the room temperature. As removed from the refrigerator swelling ratio, v, the modulus, G1, and the samples appeared to be opaque indicating crystallinity anisotropy of swelling, g, also increase. but the opacity had disappeared before readings of retardation at room temperature could be made. (X-ray Reference to sample a - N indicates the diffraction patteI~ns taken for the same samples when value of the swelling ratio and of the modulus removed fl'om the refrigerator revealed a typical when polymer a is cross-linked in the isotroamorphous scatter (fig. 9) for sample b-R7 and barely pie state. The value of g for the latter sample perceptible diffraction spots for samples b-R8.) In the following retardation-temperature cycle rates of (as well as for the other normal network heating as low as 1 ~ hours were used but it appeasample, N - 6) is, as expected, zero which red that, within the precision of the measurements, time proves the reliability of the values of g effects were unnoticeable, at least at temperatures up to measured for the oriented samples. While the 85 ~ above which such slow heating rates were avoided in order to minimize degradative processes and wandering of cross-links (23). Provided too long a stay at high temperature was avoided, the retardation was also partly a-RI2, 40 ~ b-RT, v=l reversible, as is evident from fig. 8. Some 6 retardation was still noticeable when v=l sample b-/~8 was brought (using rates of 60 ~ heating of the order of 10 ~ up to 150 ~ On swelling, the birefringence of 4 any given sample was reduced (fig. 8). Of all samples investigated only the normal networks appeared to be isotropie at room temperature. The birefringence v : 0.55 appeared to increase on increasing the 2 degree of set, ~1" The direction of high refractive index coincided with the direction of orientation. I t should be noted TE that, within the field of observation (about o 0 p I I 1 I I I i 1 i i i i 2 mm diameter observed with 10-fold magnification), the retardation was not _~ _ a-RI, ~a-R4, v=l uniform. Both the racked and the shrun58 ~ 4~ ~ ken samples showed fibrillar striations 12

-

.//-

////

(parallel to the fiber axis) of different retardation (fig. 9). l%r the shrunken samples some interfibrillar regions were completely nonbirefringent. The orientation of the fibrils was in the direction of their long axis; on rotating the microscope stage they showed almost simultaneous extinction. This pattern was essentially unmodified when the samples which had been observed at high temperature, were cooled again.

Results

8 _

~

4

o

1,2

1.4

1.6

1.8

I

1.4

1.0 2.2 2.6

5.0 5,4

The samples of polymer a offer a demonstration of the effect of Fig. 3. Stress-strain curves for unswollen and swollen samples at diffeincreased orientation of the macro- rent temperatures. A complete stress-strain cycle is reported for sampmolecules during cross-linking at les a-R12 and a-R4. Abscissa. scales shifted by integral units of 0.2 a constant dose. Samples of polymer b offer an example of the effect of the dose presence of anisotropy for oriented networks at constant orientation. While comparison of confirms the findings of Charlesby and yon different samples within the series of polymer A r n i m (12), the value of g = 0 obtained for b can be made within the limitation of the normal networks suggests t h a t also the experimental errors of the various measure- composite networks of Berry, Scanlan and ments, comparison of samples from polymer a Watson (7) m a y have been slightly anisowith samples from polymer b is certainly tropic. For these networks a value for g of subjected to a larger indetermination since about 3% was reported (7). I~esults for not only the polymers but also the type of samples of the series b indicate t h a t on incross-linking irradiation was different. As is creasing the degree of cross-linking at evident from tables 1 and 2, for samples of constant ~er, the final set, the swelling ratio the series a on increasing c%r, which measures and the modulus also increase. In this case,

8

Kolloid-Zeitschrift und Zeitschr~ft fiir Poly~nere, Band 186 9 Heft I 1.92 8

b-R7

o-R2

/

3.5 171

6

3.0

E u

5 2.5

4

E 2.0 3

~

i.~,9

I

I

I

I

320

300

I

340

1.5

/

T,K ~

Fig. 4. Stress-temperature data for sample a-R2 unswollen (@) and swollen with 66% n-hexadecane (O). The elongation at 50 ~ is indicated

1.0

b-R8 0.5

I 300

I

I

I

520

I 540

T,K ~ Fig. 6. Stress-temperature data for sample b-R7 unswollen (@) and swollen with 650/0 n-hexadecane (O). The elongation at 50 ~ is indicated 1.17

I I

(9

4

I

I

I

I

b-R6

however, t h e swelling a n i s o t r o p y f a c t o r is p r a c tically c o n s t a n t . More details of t h e stressstrain i s o t h e r m s are e v i d e n t f r o m figs. 1, 2, 3 a n d t a b l e 2. F o r unswollen s a m p l e s one can

,,__

2 1.15

I

I

.300

I

I

I

.320

I

B40

T,K~ Fig. 5. Stress-temperature data for samples b-R6 and b-R8 unswollen (@) and swollen with 65% and 61% n-hexadecanc respectively (O). The elongation at 50 ~ is indicated

o ion oo

5)

vs 1/~ p l o t (which can b e described b y t h e M o o n e y equation, eqn. [3]) followed b y an u p t u r n . This is also o b s e r v e d in n o r m a l n e t w o r k s (20) as is e v i d e n t for s a m p l e a-N. H o w e v e r , t w o i m p o r t a n t differences can be observed. F o r a n y oriented s a m p l e t h e C 2 v a l u e is smaller t h a n for a n u n o r i e n t e d n e t w o r k [which confirms t h e finding b y Oth a n d F l o r y (13)] a n d t h e u p t u r n is m a n i f e s t e d at a lower elongation t h a n for a corresponding n o r m a l n e t w o r k cross-linked a t t h e s a m e dose. This is e v i d e n t on considering t h a t t h e v a l u e of C a for n o r m a l n e t w o r k s cross-linked b y i r r a d i a t i o n is a b o u t 1.5 k g / e m ~ (reference

Greene and Ciferri, Elastic Properties of Networ.~sFormedfrom Oriented Chain Molecules

14 and sample a-N) independent of the degree of cross-linking and that the upturn takes place at elongations about 250% for sample a-N while it would be shifted to still lower elongation on increasing the dose (20). The effect of increasing orientation at a given dose (series a) is that of decreasing the value of C2 and of shifting to lower elongations the

ca E o ~:~ - 2 3 I

I

I

I

I

I

I

I

I 2 3 4.

O-R2, O- R2, b - R6, b - R6,

V=l V=O.~ V=I v = 0.35

5 6 7 8

b-R7, b - RT, b - R8, b-R8,

V=] V = 0.35 %'= I V=0.39

3

-2

I 1.0

I ~1171

1.2

14

I 1.6

I

I

I

1.8

I 2.0

1

I

'

2.2

'

'

2.4

'

2.6

Q

Fig. 7. The energy component of the refractive force at

constant pressure and at 50 ~ plotted against the elongation for different sampIes--unswollen ( 9 and swollen (O)

800

600

~

b

-

~8

400 200

~k s

E

~ ' m - . . . . _ . ~ b- R8, V--~0.4 I I

0

I

I

I

I

I

I

i

I

40

60

I

I

800 ~_ 60O 400 2OO ~0

I 20

T,

80

b - R7 I

I I00

~

Fig. 8. Retardation vs Temperature for samples b-R8 and b-~7 - - ( 9 ) increasing temperature, ( • ) decreasing temperature. Thickness of the two samples unswollen

1 mm. (O) sample b-R8 swollen with n-hexadeeane

9

upturn. The effect of increasing the degree of cross-linking at a given orientation (series b) is that of shifting the upturn to lower elongations while the C2 value is not much affected. Similar trends of C~ and of the upturn with degree of cross-linking are observed for normal networks (20). The effect of the temperature at which the stress-strain isotherm is obtained is twofold. In the linear region preceding the upturn C1 is roughly proportional to the temperature, as required b y the rubber elasticity theory, while C2 is practically unaffected. In the region of the upturn this is not so: the stresses at 30 ~ may be higher than the stress at 60 ~ (fig. 1). In particular, for sample b-R8, the upturn covers all range of extension at 30 ~ and only at 60 ~ a linear portion in the ~ r v s l / r plot can be seen. Hysteresis is present (fig. 3), as for normal networks under similar experimental conditions. In particular, for sample a-R4, one notes a reduction of hysteresis in going from 30 ~ to 60 ~ for ' experiments performed under "standard conditions" and extending well into the upturn region. The ease of swollen samples is illustrated in figs. 2 and 3. The situation for normal networks is illustrated by sample N-6. As has been established in previous investigations (14, 20) on swelling of a given normal network Ca is almost unaffected, C~ is reduced and the upturn is shifted to lower elongations. Although it is not shown in fig. 2, the hysteresis is also greatly reduced on swelling of a normal network (14). In the case of oriented samples the upturn is similarly shifted to lower elongations and in most cases it covers all practical ranges of measurements. The stress for swollen samples can actually be higher than for the corresponding unswollen ones, the cross-over point is shifted to lower elongations on increasing the modulus. Hysteresis is not affected b y swelling (fig. 3) in contrast to the behavior of normal networks (14). The stress-temperature experiments were performed independent of the stress-strain ones, since, in this way, greater precision is gained. Consideration of the results reported on table 3 and fig. 7 shows that the energy component, (OH/OL)~,T at first increases with elongation until a downturn is reached, which, for unswollen samples, roughly corresponds to the appearance of diffraction spots in the X-ray pattern. On swelling this downturn is shifted to lower elongation. A super-

Kolloid-Zeitschrift und Zeitschrift fiir Polymere, Band 186 9 Heft I

10

ficiaL correlation between this downturn of the energy component und the upturn of the stress-strain curves is evident on inspection of figs. 1, 2 and 7. Of particular interest seems the fact that this correlation holds also in eases of swollen samples : both the upturn and the downturn are shifted to lower elongations

when a given sample is swo~ie~ with n-b_ex~decane. However, the re~'~aJ_ts a r e no~ accurate enough to establish if t~ere;id'i~p.v quantitative correlations between th6 eIa~gat%ns at which the upturn 'and the down{urn,~begin. The calculations of the energy Component at constant volume, re, rests on the assump-

Table 3 Stres>Temyerature D~ta for Samples Unswollen and Swollen with n-Hexadeeane 1)

~,

\ OT h,, L lc~

~

~

TK

~,,~

o~3--1

7-

1,40 1.50 1.71 1.92

7.6 11.4 16.6 27.5

3.485 4,753 6,303 7.666

Sample a - ~ 2 Unswollen 1.03 0,12 1.07 0,09 0.94 0.05 - - 1.22 (0.03)

1.29 1.40 1.48 1.56 1.60 1.65 1.75

4.6 6.8 8.3 10.2 11.1 12.5 16.4

2.642 3.192 4.060 4,389 4.502 4.812 5.455

Sample a-R2 Swollen, v = 0.34 1.16 0.23 0.99 0.15 1.38 0.12 1.10 0.09 0.92 (0,08) 0.77 (0.07) 0.16 (0.06)

0.21 0.16 0.22 0.16 (0.12) (0.09) (--0.03)

1.15 1,25 1.35 1.45 1.55

3.2 5.5 8.9 11.7 17.7

1.554 2.118 2,796 3233 3,678

Sample b-t~6 Unswo]len 0.52 (0.41) 0.34 (0,22) --0.08 (0,15) --0,55 (0.10) --2,04 (0.08)

(--0.08) (--0.06) (--0.18) (--0.27) (--0.63)

1.17 1.242 ) 1.30

4.4 8.3 10.3

1.410 2,064 2.380

Sample b-R6 Swollen, v = 0,35 --0.01 (0.44) --0.62 (0.29) --0.95 (0.22)

(--0.45) (--0.59) (--0.62)

1,36 1.472) 1.69 1.81 2.06 2,20 2.43 2.56

2.6 3.0 4.7 5.1 8.1 9.5 14.4 16.7

1.228 1.348 1.889 2.075 2.698 2.874 3.230 3.483

Sample b-I17 Unswollen 0.39 0.14 0,38 0.10 0.37 0.06 0.43 0.04 0.08 (0.03) --0.19 (0.02) - - 1.42 (0,02) - - 1.91 (0.01)

0.18 0.18 0.I4 0.17 (0.00) (--0.09) (--0.46) (--0.56)

1.37 1.50 1.70 1.90 2.092)

1.8 2.3 3.4 5.2 7.2

0.862 1.110 1,320 1,636 1.821

Sample b-R7 Swollen, v = 0.35 0.280 0.17 0.367 0.11 0.222 0.07 --0.043 (0.05) --0.505 (0.03)

0.16 0.22 0.10 (--0,08) (--0.31)

1.35 1.45

12.1 20.5

2,595 3.319

Sample b-R8 Unswollen - - 1.31 (0.15) --3.a0 (O.iO)

(--0.66) ( - - t.09)

1.17 1.26 1.362 )

4.6 7.6 14.8

1.aao 1.906 2.567

Sample b-~8 Swollen, v = 0.39 --0.15 (0.44) --0.55 (0.26) --2.21 (0.17)

(--0.55) (--1.03)

0.18 / 0.14 0.10 ( - - 0.19)

Av = 0.14

Av = 0.19

Av = 0.17

Av = 0.16

(--0.62)

1) r in kg cm -~, T in ~ T = 323. 2) Measurements from which these results were derived have not been included in Figure 5 and 6.

Greene and Ciferri, Elastic Properties of Networks Formed from Oriented Chain Molecules

Fig. 9. Wide angle X-ray diffraction patterns at 25 ~ for a raeked uncross-linked sample (a), for the shrunken b-R7 sample unswollen (b) and for the shrunken b-l~8 sample, swollen with ~ 60O/o n-hexadeeane (e). Sample b-l~8 photographed in the polarizing microscope: (d) racked, 25 ~ (e) shrunken, 50 ~ (magnification • 70)

11

12

Kolloid-Zeitschrift und Zeitschriflfiir Polymere, Band 186 9Heft 1

tion that eqn. [5] is valid which, in turn, depends on the validity of eqn. [1]. Although the shape of the stress-strain isotherm for unswollen oriented networks in the region preceding the upturn is closer to eqn. [1] than in the case of the normal network, we have seen that the agreement with theory is apparent; the presence of anisotropy, in particular, makes the analysis based on eqn. [5] somewhat inconsistent. No better solution would be that of the alternate (1, 2) method for calculating /e// based on the relationship : T(~T) (6) which specifically rests on the assumption of isotropy. As a matter of fact we have calculated /e// values according to eqn. [6] and found these to agree, in the region preceding the npturn, with the results obtained according to eqn. [5] provided the term @ is added to the right side of eqn. [6]. This latter term has been shown (19) to represent the amount b y which eqn. [6] underestimates /e/l" We observe, however, that in the region preceding the upturn ]e/] values reported in table 3 are not essentially different for the different samples, in spite of the fact that these samples vary in their anisotropy. Because of this and considering the large experimental error affecting ]e// (table 3) we believe that the use of eqn. [5] would still lead to a satisfactory determination of ]e/]. This confirms the fact that ]e/] is not very sensitive to the details affecting the stress-strain isotherm as has been established in cases of normal networks unswollen and swollen with n-hexadecane (24) and b y the analysis of Roe and Krigbaum (25). In this light, it appears that in the region preceding the upturn the ratio ]e// is, within the limits of experimental errors, unaffected b y ~ or b y the solvent, the average value, i.e. 0.17, completely agrees with the value, 0.18, determined for normal networks (24, 25). The calculated ]e/] values in the region of the upturn are unreliable. These values have been enclosed in parenthesis in table 3 only for comparative purpose. They would indicate a decrease (25) of ]e/] with a. This unreliability is due to the failure of eqn. [5] to apply to situations where deviation from either eqn. [1] or [3] becomes important and where, as evidenced b y the occurrence of diffraction spots in the X-ray pattern, crystallization, and therefore large intermolecular energy effects are present.

Discussion

As far as the essential thermodynamic properties are concerned (the large entropy contribution of the refractive force and even the small positive contribution from the intramoleeular energy) the oriented networks exhibit, in the region preceding the upturn, rubber-like elasticity. However, when details of the stress-strain isotherm and of the swelling behavior are considered, deviations not only from the rubber elasticity theory (eqn. [1]) but also from the behavior of normal networks are clearly evident. Of these deviations the more interesting is that of the anisotropy of oriented networks. From the melting point determinations of Roberts and Mandelkern (15) and of Oth and Flory (13) it would appear that the melting point of our unstressed oriented networks should lie below 30 ~ Also, according to these authors, our sample b-R8 should melt at a lower temperature than sample b-R7 which has a lower concentration of cross-links although, from theoretical considerations, one might have expected the reverse (3). Yet, even at 85 ~ the birefringence of the former is higher than that of the latter. It could be that, even after the melting has occurred, labile structures are preserved and the complete disorientation of the chains is a slower process for the more cross-linked sample b-R8 than it is for sample b-RT. The decrease of the birefringence with temperature would be coherent with this interpretation. The lack of time effects and the partial reversibility of the birefringence would, however, conflict with it. Even more striking is the failure of the birefringenee to disappear after the samples are maintained for a relatively long time at temperatures up to 150 ~ or when they are swollen with n-hexadecane. The results from equilibrium swelling measurements confirm the anisotropic character of the oriented networks. For all samples the swelling anisotropy factor increases with the permanent set, as does the birefringence, with the exception of sample b-R7. For this sample, however, deviations could be accounted for on the basis of the lower degree of cross-linking (12). The conclusion seems evident that the anisotropic character of these networks can be regarded as permanent, at least in the limits in which our measurements were performed. As to the exact nature of the structural factors determining the anisotropy, only speculations can be made. The increase of anisotropy with permanent set suggests that

Greene and Ciferri, Elastic Properties of Networks Formed from Oriented Chain Molecules

on increasing the set a higher degree of the original fibrillar orientation is maintained in the shrunken sample. This orientation m a y be peculiar to the network or to residual oriented erystMlization. The birefringenee measurements cannot discriminate between orientation and crystallization and, except for sample b-RS, for which very faint diffraction spots could be detected at 25 ~ the other samples gave a typical amorphous scatter. However, consideration of the parscrystal theory of Hosemann (26) suggests that diffraction phenomena m a y not be able to distinguish between a paracrystalline lattice and an amorphous network. The presence of residual oriented crystallization (at least for sample b-R8 which shows a marked decrease of birefringenee with temperature) at temperatures well above 30 ~ would not necessarily contrast with the melting point determinations quoted above. This residual crystallization m a y be very small and associated with regions of inhomogeneity within a given sample. We note that Hammer, Brandt and Peticolas (27) have reported another case in which a long range pattern established during crystallization is mainrained after the system has been cross-linked and melted (melting being assumed b y the disappearance of erystallinity as indicated b y X-ray). This is the case of polyethylene crystallized in the unstretehed state for which the long range pattern was spherulitie rather than fibrillar. Another interesting feature presented b y our oriented networks is the increase of the value of the swelling ratio when the orientation is increased at constant dose (series a). This agrees with the observation of Roberts and Mandel]cern (15) that cross-linking is more effective for oriented than for normal networks. Even apart from this effect, the amount of solvent which a network will imbibe at equilibrium is expected to depend upon the arrangement of the chains during cross-linking as is deduced from consideration of the equations governing equilibrium swelling m an excess solvent (3). The essential reason for this is the fact that the term ( ~ / ~ ) , cf. eqns. [1] and [2], depends npon the particular arrangement of chains during network formation although no quantitative evaluation of this effect was given (3, 15). The increase of the modulus C1 with orientation could be expected from the increase of the swelling ratio and of the swelling anisotropy factor. Not obvious, however, is the fact, that samples with higher swelling anisotropy are characterized by a

13

lower value of 02 . For normal networks similar variations of O1 and O2 could be expected on the basis of a better approach to equilibrium conditions (14), of deviations from the gaussian behavior or on the basis of the model of different networks connected in series (28). For our oriented networks a better approach to equilibrium seems unlikely in view of the fact that hysteresis is far from vanishing even before the upturn region (fig. 3). The non-gaussian effect could be suspected in view of the fact that gaussian networks are expected to be isotropie (of. introductory section) and of the large permanent set acquired b y the samples. The model of different interconnecting networks and the limiting ease of a network "filled" b y its own erystallites is supported b y the fact that regions of different retardation could be observed within a given sample. Thus the details of the stress-strain isotherm also offer some support to the view that our oriented networks Contain regions of inhomogeneity which are more oriented than the remaining matrix. Depending upon the experimental condition, these regions m a y be crystalline since, at the same density of cross-linking, regions in which chains are more oriented must possess higher melting point than the matrix. However, during deformation up to the upturn no important (further) crystallization takes place in view of the fact that the effect of temperature before the upturn is that expected on the basis of rubber elasticity. Unfortunately, a detailed treatment which could explain on this basis the details of the stress-strain isotherm as well as the swelling anisotropy is not available. It is interesting to speculate whether these regions may be centers which give the network that "memory" of the original orientation which is associated with the phenomenon of spontaneous relongation on crystallization (13, 16). It thus appears that the different dependence of stress on strain (in the region preceding the upturn) makes an oriented networks easily distinguishable from a normal network. This is an apparent contrast with the theoretical predictions set forth in the introductory section. However, in view of the large non-equilibrium effects on the stress-strain isotherm and in view of the anisotropic character of our oriented networks, it is evident that there is not much justification in carrying too far a comparison between our results and the equilibrium theory which presupposes isotropic behavior. Since we have restricted our observations to oriented natur-

14

Kollold-Zeltschrifl und Zeitschrift fi~r Polymere, Band 186 9 Heft I

al rubber networks prepared as set forth in the experimental section, we cannot exclude that a network formed from oriented chain molecules can be isotropic in conditions other than the ones we have adopted here. It is in these other conditions that comparison with the theory should be eventually made. We turn now our consideration to the upturn region which has been shown to roughly correspond to the region of the downturn of the energy component (dH/dL)~, T" The shifting of the upturn to lower elongation with increasing orientation could be expected from the parallel increase of the swelling ratio, of the swelling anisotropy factor and of the modulus (20). In particular, one would expect that, other conditions being equal, for samples in which a higher orientation is preserved, less overall strain is necessary to reach the upturn region. As far as the structural factors responsible for the upturn are concerned, we observe that, in the case of normal networks, the upturn has been associated with the occurrence of stressinduced crystallization or, alternatively, to non-gaussian behavior (1, 20). l~ecently Mullins (20) has shown that, for normal networks, either an increase of the degree of cross-linking or of the amount of the solvent absorbed, have the result of shifting the upturn to lower elongation. He was able to show that such effects could be quantitatively explained b y the non-gaussian theory. Similar effects of the degree of crosslinking and 0fthe solvent have been observed for our oriented networks 9 However, from the appearance of diffraction spots in the region of the upturn and from the effect of the temperature in shifting the upturn to higher elongations (fig. 1) and in decreasing the hysteresis (fig. 3), we can conclude that, for unswo]len oriented networks, the occurrence of the upturn is accompanied b y the occurrence of stress-induced crystallization. A correspondence of the upturn to the downturn of the energy component would then be expected since we can write (for small volume changes) (1, 2)

and the decrease of (aH/cSL)_ T with ~ ma~ be ascribed to a decrease of volume and energy which accompanies stress-induced crystallization (1). In the case of swollen networks one would expect the presence of the solvent to reduce any tendency toward

crystallization and indeed crystallization under stress is not evidenced b y X-ray. From these considerations, and from the fact that the upturn is apparent at lower elongation for swollen networks than for the corresponding unswollen networks, one could conclude that non-gaussian behavior is the primary phenomenon responsible for the upturn, crystallization being a secondary phenomenon. Against this conclusion is however the fact that also in the case of swollen networks we observe a downturn of (6H/6L)p T which m a y be associated with crystallization. Lacking a quantitative study of the relation between the upturn and downturn even in the case of normal networks, it is difficult to assess unambiguously whether crystallization or non-gaussian behavior is the primary phenomenon responsible for the upturn. It is, however, clear that in the region of the upturn energy effects become very important. To conclude, the region of elongations in which essentially entropy effects determine the elastic properties of networks formed from oriented natural rubber molecules is considerably smaller than for normal networks cross-linked at the same dose. In this region small intramolecular energy effects, as measured b y the ratio /e/i, are similar to those observed in normal networks. After this region, energy effects become very important. Even in the range of essentially entropy elasticity, deviations from the postulutes of the conventional rubber elasticity theory and from the behavior of normal networks are observed, such as the anisotropy in the rest and in the swollen state. While the role of inhomogeneity regions where chain molecules have greater tendency to crystallize than in the matrix has been emphasized, a detailed description of the structural factors responsible for the anisotropy, and the validity of these results for other macromolecular networks formed in the oriented state, await further investigation. Acknowledgment

We wish to express our appreciation to Dr. K . J. Smith, Jr. for his interest in this work and for the benefit of interesting and clarifying discussions9 Summary In order to investigate the effects of particular arrangements of macromoleculesduring cross-linking on the elastic properties of the network, highly oriented

Greene and Ciferri, Elastic Properties of Networks Formed from Oriented Chain Molecules fibrous naturM rubber samples were cross-linked with high energy radiation and shrunk in boiling water. Stress-strain-temperature measurements were performed on the shrunken networks, the deformation being an unidirectional extension in the direction of orientation. Additional measurements of equilibrium swelling in n-decane, of birefringenee and wide angle X-ray diffraction patterns for unstretched and for stretched samples were obtained. The mMn results can be summarized as follows : the amount of solvent absorbed at equilibrium swelling, the ease of deformation in the direction of orientation and the range of elongation in which essentially entropy effects determine the elastic properties of the networks, are considerably smaller than for networks cross-linked in the isotropic state at the same dose. In this range of elongation, a small positive component of the intramolecular energy, similar to that observed for normal networks, is observed. At moderate elongation an upturn of the stress-strain isotherm is observed which roughly corresponds to a downturn of the energy component (dH/~L)p,T. Both the upturn and the downturn are shifted to lower elongations when a given sample is swollen with n-hexadecane. Even in the elongation region preceding the upturn, deviations from the behavior of networks cross-linked in the isotropic state and from the rubber elasticity theory are observed. Most noticeable differences are the facts that the oriented networks are anisotropic (as evidenced by birefringence and equilibrium swelling measurements) and that the shape of the stress-strain isotherm is adequately represented by the strain function a - - -~ of the rubber elasticity theory. While the role of inhomogeneity regions where chain molecules have greater tendency to crystallize than in the matrix has been emphasized, a detailed description of the structural factors responsible for these phenomena and the validity of these results for other networks formed in the oriented state, await further investigation.

Zusammen/assung Um Effekte der besonderen Anordnung der Makromolekiile wh,hrend der Vernetzung auf die elastischen Eigenschaften des Netzwerkes zu untersuehen, warden hoehorientierte Naturkautsehukproben mit Strahlung hoher Energie vernetzt und in koehendem Wasser geschrumpft. Zug-Dehnungs-Verhalten in Abhs yon der Temperatur wurden an diesen gesehrumpften Netzwerken durchgefiihrt, wobei die Deformation eine einachsige Dehnung in Richtung der Orientierung war. Zus~tzlieh erfolgte die Untersuehung der Gleichgewichtsquellung in n-Dckan, der Doppelbreehung und der Weitwinkelstreuungf/Jr ungestreckte and gestrecktc Proben. Die wesentlichen Resultate lassen sich wie folgt zusammenfassen : Der absolute Betrag an adsorbiertem Lhsungsmittel im Gleiehgewieht bei tier Quellung, die Leichtigkeit der Deformation in Orientierungsrichtung and der Bereich der Verli~ngerung, in dem im wesentlichen die Entropieeffekte die elastischen Eigenschaften des Netzwerks bestimmen, sind betr&chtlich kleiner als bei Netzwerken, die mit gleicher Strahlungsdosis im isotropen Zustand vernetzt wurden. Innerhalb dieses Bereichs der Verli~ngerung wird ein kleiner positiver Anteil an zwischenmolekularer Energie beobaehtet ~hnlich dem bei normMen Netzwerken. Bei mittlerer Verli~ngerung ist ein Anstieg dcr Zug-Dehnungsisotherme zu bemerken, welche grob dem Abfal] der Energiekomponente (dH/dL)p,T entsprieht. Beides, Anstieg and Abfall, verlagern sich zu geringeren Verl/~ngerungen, wenn die entsprechende Probe mit n-Hexadekan

15

gequollen wird. Gerade in dem Verlgngerungsbereich, der dem Anstieg vorangeht, sind die Abweiehungenvom isotrop vernetzten Netzwerk and yon der Theorie der GummMastizitgt zu beobaehten. Die bemerkenswertesten Unterschiede beruhen darauf, dab die orientierten Netzwerke anisotrop sind (wie auch Doppelbrechung and Gleichgewicbtsquellungandeuten) und dab die Gestalt der Zug-Dehnungsisotherme dutch die

Dehnungsfunktion a

1

a g der

Gummitheorie

gegeben wird. Wghrend die Rolle der inhomogenen Bereiche, in denen die Kettenmolekiile grhBere Tendenz zur Xristallisation besitzen als in den iibrigen, herausgestellt ist, erfordert einc eingehende Beschreibung der strukturellen Faktoren, die fiir diese Phgnomene und die Gfiltigkeit dieser Resultate fiir andere Netzwerke, die im orientierten Zustand gebildet wurden, Verantwortlieh sind, weitere Untersuchungen.

Re/erences 1) Treloar, L. R. G., The Physics of Rubber Elasticity, 2rid ed. (Oxford, 1958). 2) Ci/erri, A., J. Polymer Sci. 54, 149 (1961). 3) lVlory, P. J., J. Amer. Chem. Soe. 78, 5222 (1956). 4) Mason, P., J. Chem. Physics 35, 1523 (1961). 5) Lodge, A. S., Kolloid-Z. 171, 46 (1960). 6) Andrews, R. D., A. V. Tobolsky, and E. E. Hanson, J. App]. Physics 17, 352 (1946). 7) Berry, J. P., J. Scanlan, and W. F. Watson, Trans. Faraday Soe. 52, 1137 (1956). 8) t~lory, P. J., Trans. t~araday Soc. 56, 722 (1960). 9) Scott, K. W. and R. S. Stein, J. Chem. Physics 21, 1281 (1956). I0) Scanlan, J. and W. F. Watson, Trans. Faraday Soc. 54, 740 (1958). ll) Scanlan, J., Trans. Faraday Soe. 57, 839 (1961). 12) Charlesby, A. and E. yon Arnim, J. Polymer Sei.

25, 151 (1957). 13) Oth, J. F. M. and P. J. Flory, J. Amer. Chem. Soc. 80, 1295 (1958). 14) Ci/erri, A. and P. J. Flory, J. Appl. Physics 30, 1498 (1959). I5) Roberts, D. E. and L. Mandelkern, J. Amer. Chem. Soc. 80, 1289 (1958). i6) Mandelkern, L., D. E. Roberts, A. F. Diorio, and A. S. Posner, J. Amer. Chem. Soe. 81, 4148 (1959). 17) Oth, J. F. M., Kolloid-Z. 171, I (1960). 18) Speakman, P. T., Trans. Faraday Soe. 57, 518 (1961). 19) Ci/erri, A., C. A. J. Hoeve, and P. J. ~'lory, J. Amer. Chem. Soc. 83, 1015 (1961). 20) Mullins, L., J. Appt. Polymer Sci. 2, 257 (1959). 21) Bek~edahl, N. and L. A. Wood, Rubber Chem. Teeh. 14, 347 (1941). 22) Eglo~, G., Physical Constants of Hydrocarbons, Vol. 5, (New York, 1953). 23) Voorn, M. L. and J. J. Hermans, J. Polymer Sci. 35, 113 (1959). 24) Ci/erri, A., )r Chem. 43, 152 (1961). 25) t~oe, R.-J. and W. R. Krigbaum, J. Polymer Sci. 61, 167 (1962). 26) MeCullough, R. L. and R. Hosemann, (to be published). 27) Hammer, C. F., W. W. Brandt, and W. L. Peticolas, J. Polymer Sci. 24, 291 (1957). 28) Mullins, L. and N. R. Tobin, Proc. 3rd l~ubber Technology Conf. 397 (1954). Authors' address : A . Greene a n d A . CiJerri, B a s i c R e s e a r c h D e p t . , C h e m s t r a n d R e s e a r c h Center, I n c . , l~eseareh T r i a n g l e P a r k , P. O. B o x 731, D u r h a m , N o r t h C a r o l i n a (USA)